“Winning that way, we suffered a lot in the first half, especially in the last 20 minutes,” Guardiola said. “The opponents had a good side, so strong in front, we could not press. They played long balls, attacked the channels.

“They are taller than us and stronger than us. That can happen. The last 20 minutes we were flat, not the rhythm we need but it is normal. That is why I am delighted to win in that way. Everything is so tough.”

Wilson’s equaliser was reward for a Bournemouth team who finished the first half on top, and Guardiola admitted he struggled to find a solution until a mazy run from Sterling – which ended with his shot rebounding off the post – lifted City spirits eight minutes into the second half.

“We spoke about it at half-time but my speech was ridiculous,” Guardiola said. “It didn’t work because the first five or 10 minutes was like the first half.

“In the first half Raheem was not there but then he makes a slalom and changes the game.”

Before Sterling’s intervention, there was a growing sense in the Etihad that this could be the day City dropped points at home for the first time this season, fuelled by the threat Wilson and Joshua King were posing when Bournemouth broke forward.

“We believed before the game, we believed at half-time,” Cherries boss Eddie Howe said. “We had a good spell before half-time where we scored a good goal. The plan was going the way we wanted it to.

“The second and third goal both hurt us in different ways, and the third goal probably put the game to bed. Credit to the players for sticking to what we wanted them to do.”

Though City were ultimately deserving winners, Howe could be unhappy with the City goals, all of which came from rebounds and second balls.

“Usually when you come here you are vulnerable to the individual quality,” Howe said. “I thought the goals were scrappy from our perspective and avoidable.”

Guardiola had the busy festive period to come in mind as he made five changes to his side from the midweek win over Lyon, with Sergio Aguero not in the matchday squad at all and David Silva coming on as a second-half substitute.

“Doctors, physios, instinct, what I see, many reasons,” Guardiola said about those who did not play. “If you ask me why Sergio don’t play, David don’t play, I will tell you each one. You finish Boxing Day and January is tougher and February again.”

City can now focus on preparing for Watford on Tuesday night while their rivals face difficult matches on Sunday, with Liverpool playing Everton in the Merseyside derby while Arsenal and Tottenham meet in north London.

“I think it is too early to see how decisive it is,” Guardiola said of City’s advantage. “We didn’t finish (this round) but we played today and tomorrow both or one of Arsenal and Tottenham will drop points.

“We will prepare for the game at Watford and watch the games. Our success in the last 15 months is (because) we don’t care too much about the other sides. Always I tell them, expect the best from the other sides, expect that Liverpool will drop minimum points, so we have to win games.”

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